Bubble tree compactification of moduli spaces of vector bundles on surfaces

• Autorzy: Dimitri Markushevich , Alexander Tikhomirov , Günther Trautmann
• Języki publikacji: EN

Abstrakty

EN

We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes c 1 = 0, c 1 = 2 on the projective plane is studied in more detail. Proofs are only indicated and will appear in separate papers.

Słowa kluczowe

EN

Instantons; Vector bundles; Coherent sheaves; Moduli spaces of sheaves; Donaldson-Uhlenbeck compactification; Monads; Serre construction; Fulton-McPherson compactification

Kategorie tematyczne

• 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli
• 14D20: Algebraic moduli problems, moduli of vector bundles
• 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 4
• Strony: 1331-1355

Daty

wydano

2012-08-01

online

2012-05-31

Twórcy

autor

Dimitri Markushevich

• Université Lille 1,

autor

Alexander Tikhomirov

• Yaroslavl State Pedagogical University,

autor

Günther Trautmann

• Universität Kaiserslautern,

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Identyfikatory

DOI

10.2478/s11533-012-0072-0